Answer to Question #272959 in Microeconomics for barbra

Question #272959

Robinson's preferences between apples (a) and bananas (b) are expressed by the following:

 

U = (a+2)0.5(b+1)0.5

 

(a) Show that Robinson's indifference curves are negatively sloped.

(b) Are they convex to the origin? Explain.


1
Expert's answer
2021-11-30T10:15:52-0500

a)U = (a+2)0.5(b+1)0.5

Let (a+2) be x and (b+1) be y.


U becomes;

U="x^{0.5}y^{0.5}"


"MU_{x}=0.5x^{-0.5}y^{0.5}"


"MU_{y}=0.5x^{0.5}y^{-0.5}"


"MRS=\\frac{MU_{x}}{MU_{y}}"


MRS is the slope of the indifference curve at any single point along the curve.


"=" "\\frac{0.5x^{-0.5}y^{0.5}}{0.5x^{-0.5}y^{0.5}}=\\frac{y}{x}"


b)The indifference curves will be convex to the origin because, as one consumes more of good y, they will consume less of good x.


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